Abstract
Two different constructions generating the low-energy expansion of genus-one configuration-space integrals appearing in one-loop open-string amplitudes have been put forward in refs. [1,2,3]. We are going to show that both approaches can be traced back to an elliptic system of Knizhnik-Zamolodchikov-Bernard(KZB) type on the twice-punctured torus.
We derive an explicit all-multiplicity representation of the elliptic KZB system for a vector of iterated integrals with an extra marked point and explore compatibility conditions for the two sets of algebra generators appearing in the two differential equations.
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Broedel, J., Kaderli, A. & Schlotterer, O. Two dialects for KZB equations: generating one-loop open-string integrals. J. High Energ. Phys. 2020, 36 (2020). https://doi.org/10.1007/JHEP12(2020)036
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DOI: https://doi.org/10.1007/JHEP12(2020)036